Sunday, August 16, 2015

A riff on the circle Hough transform applied to a 3 x 3 array of rings. The maxima (brightest points) correspond to detection of ring centers, and all arcs arcs are essentially pixelwise convolutions of subsampled rings with the source image. Cycling the phase of the subsampling provides the temporal variations.

We were experimenting with a continuous version of a Hough transform to find rings in electron diffraction images, in order to quantify the sharpness of their radial profile. But it was a lot of fun to use the transform to generate variations on arrays of arrays of circles.

Sunday, June 28, 2015

This is variation of Euler's identity, for a rotation of tau radians. It states that a full rotation always brings an object back to its original state. Its beauty and utility lie in the fact that rotations can be expressed as products (or powers) of unit vectors on the complex plane.

Thursday, March 19, 2015

In this case, since the orders that exercise the entire control are in the memory, a higher degree of flexibility is achieved than in any previous mode of control. Indeed, the machine, under the control of its orders, can extract numbers (or orders) from the memory, process them (as numbers!), and return them to the memory (to the same or to other locations; i.e. it can change the contents of the memory -- indeed this is its normal modus operandi. Hence it can, in particular, change the orders (since these are in the memory!) -- the very orders that control its actions. Thus all sorts of sophisticated order-systems become possible, which keep successively modifying themselves and hence also the computational processes that are likewise under their control. In this way more complex processes than mere iterations become possible. Although all of this may sound far-fetched and complicated, such methods are widely used and very important in recent machine-computing -- or, rather, computation-planning -- practice.

Of course, the order-system -- this means the problem to be solved, the intention of the user -- is communicated to the machine by "loading" it into the memory. This is usually done from a previously prepared tape or some other similar medium.

This short book is an amazingly clear, succinct overview of computer architecture and operation. A few terms don't follow current usage, but the content is fully modern. It is a largely complete foundation for robopsychology.

The Computer and the Brain is an important historical document, from the era in which the computational theory of the mind-brain was introduced and explored in detail. It’s a landmark in the history of computing, psychology, and neuroscience, and it’s required reading for anyone interested in the foundations of those disciplines.